1)If I head across a river paddling my canoe at 6km/h N, but the river current is moving at 3km/h E, determine the speed and direction of my canoe relative to the shore.

Jul 20th 2008, 10:26 PM

Chop Suey

Given:
$\displaystyle v_{cr} = 6 km/h\ N$

$\displaystyle v_{re} = 3 km/h\ E$

$\displaystyle v_{ce} =\ ?$

cr: canoe with respect to river
re: river with respect to earth
ce: canoe with respect to earth

First, for speed remember that in order to get $\displaystyle v_{ce}$, I need to have a velocity who subscript starts with c and ends with e. Thus:

$\displaystyle v_{ce} = v_{cr} + v_{re}$

Use Pythagorus theorem to find v_{ce} now:

$\displaystyle v_{ce}^2 = v_{cr}^2 + v_{re}^2$

Second, for direction, use tangent ratio:

$\displaystyle \tan{\theta} = \frac{v_{cr}}{v_{re}}$

Be careful though! When you get the angle, make sure you state the direction correctly. If you found the angle using this ratio:

$\displaystyle \tan{\theta} = \frac{v_{cr}}{v_{re}}$

Then direction is: The direction of $\displaystyle v_{cr}$ of The direction of $\displaystyle v_{re}$.

Jul 24th 2008, 09:56 PM

jerryflower

triangle problem solving

This question is related to the Pythagoras theorem. You can solve this problem by using Pythagoras theorem. It will be easy to solve when you apply it in the question.
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